Institute of Fundamental Technological Research

The NUMPRESS System has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. The program consists of (i) an analytical module for analysis of forming processes with the finite element method, (ii) an optimization module controlling execution of the analytical module and performing optimization with respect to selected process parameters, in both deterministic and robust formulation, (iii) a reliability analysis module controlling execution of the analytical module to assess how random distribution of design parameters affects forming results, and (iv) a graphical user interface enabling communication between modules and easy definition of design parameters and optimization criteria. The analytical module consists of two independent programs up to the user's choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic and elastic-viscoplastic shells. Both programs are interfaced to a well-known commercial graphical pre- and postprocessor GiD. Fundamentals of formulations employed in the system and numerical examples are presented in the paper.

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

The main objective of this paper is to improve stability conditions, uniqueness and convergence of numerical analysis of metal forming processes with contact constraints enforced by the penalty method. A commonly known drawback of this approach is the choice of penalty factor values. When assumed too low, they result in inaccurate fulfillment of the constraints while when assumed too high, they lead to ill-conditioning of the equations system which affects stability and uniqueness of the solution. The proposed modification of the penalty algorithm consists in adaptive estimation of the penalty factor values for the particular system of finite element equations and for the assumed allowed inaccuracy in fulfillment of the contact constraints. The algorithm is tested on realistic examples of sheet metal forming. The finite element code based on flow approach formulation (for rigid-plastic and rigid-viscoplastic material model) has been used.

Contact modeling, Penalty approach, Metal forming, Deep drawing

The objective of the paper is the sensitivity analysis of deep drawing simulations using flow approach with respect to any design parameter. The sensitivity analysis is being implemented into the MFP code developed by IPPT PAN under project Numpress. First, the finite element formulation of flow approach in drawing simulations is presented. The mathematical formulation includes the consistent tangent viscosity matrix. As it is shown in the final sensitivity formulation, the tangent viscosity matrix is necessary in sensitivity calculations. Unfortunately the tangent matrix is asymmetric. The influence of the asymmetric contributions to viscosity matrix in sensitivity analysis is considered. The semi-analytical Direct Differential Method is used. This means that design derivatives of some terms are estimated by finite difference method and next substituted into analytical sensitivity formula. The mathematical formulae and the algorithm to build consistent tangent matrix and to perform sensitivity analysis are presented.

deep drawing, flow approach, sensitivity analysis

The main objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with viscoplastic and plastic material models. In this paper, the problem of convergence and uniqueness of the problem of non-linear simulation of sheet metal forming processes modeled using rigid-viscoplastic material model is considered. In the numerical simulation of the deformation process MFP2D and MFP3D Finite Element programs were used. The simplicity of the algorithm is the main advantage of these codes, the Direct Differentiation method and optimization modules can be implemented in the source code. The numerical instability caused by high values of the condition number of the main system of equations is the main disadvantage of the codes. The penalty approach contact model used in the program makes the stiffness matrix condition number worse.

finite element method, sheet metal forming, computational stability, flow approach

The objective of this paper is to improve stability conditions, uniqueness and convergence of the flow approach algorithm with rigid-viscoplastic and plastic material models. Two numerical codes, MFP2D and MFP3D, were used previously for practical industrial solutions (Sosnowski, 2001; Sosnowski, 1995; Sosnowski et al., 1992). Relative simplicity of both the codes allowed to include “exact” sensitivity calculations by direct differentiation method. This made it possible to perform very effective optimization of the whole sheet metal forming process simulation. One of significant drawbacks of rigid-viscoplastic shell approach is poor stability and convergence due to relatively high values of the condition number of the resulting system of equations. The reasons include the absence of elasticity terms in the constitutive material law and asymptotic character of the relationship between viscosity and effective plastic strain rate. Approximate character of the contact modeling (penalty approach) also affects conditioning of the system. This drawback can be overcome by some measures proposed in this paper.

sheet drawing, flow approach, matrix condition number

In this paper the numerical method for prediction of fatigue life of structure is presented. The fmite element model-ling and damage parameter calculation are based on the algorithm de-scribed originally by Chaboche (1987), Luccioni et al. (1996) and 011er et al. (2005). This al-gorithm is simplified, i.e. the Goodman relationships between the mean and stress amplitude are included. It is extended and applied for simulation of crack propagation in the rotor shaft. The mate-rial constitutive model includes plastic effects and damage. The S—N fatigue func-tions taken from experiment are modi-fied so as to be dependent on the real ratio between minimum and maximum stress in the critical zones. So the coupling between damage, plastic-ity and fatigue is taken into account.

metal fatigue, damage mechanics

W niniejszej pracy rozważamy problem zbieżności i jednoznaczności rozwiązania nieliniowego problemu symulacji procesów tłoczenia blach modelowanych z wykorzystaniem sztywno-lepkoplastycznego modelu materiału. Do symulacji wykorzystujemy programy MFP2D i MFP3D sprawdzone w kilku zastosowaniach przemysłowych. Zaletą obydwóch kodów numerycznych jest względna prostota algorytmu, a co za tym idzie możliwość dokładnej analizy wrażliwości i optymalizacji procesu tłoczenia blach. Niestety oba programy mają poważną wadę związaną z przyjętym modelem materiału. W trakcie obliczeń obserwujemy niestabilność wywołaną stosunkowo wysokim wskaźnikiem uwarunkowania macierzy układu równań. Dodatkowo przyjęty model kontaktu zawierający funkcję kary pogarsza wskaźnik uwarunkowania macierzy sztywności. Celem badań jest między innymi poprawienie tego wskaźnika.

tłoczenie blach, teoria plastycznego płynięcia, wskaźnik uwarunkowania macierzy

This paper presents NUMPRESS System that has been developed in IPPT PAN as a result of a project financially supported by European Regional Development Fund (within the Innovative Economy Programme) and is dedicated to small and middle enterprises dealing with sheet metal forming. It seems undoubted that efficient design of an industrial sheet forming process requires reliable computer simulations and a tool for numerical optimization of the process parameters. It has to be also admitted that. among small and medium enterprises (SME) in this industrial branch, there are many who do not use any such numerical tools in their practice.
Computer simulation of sheet metal forming processes is a very specific branch of computational mechanics. Finite element systems dedicated strictly to this kind of processes are needed and actually present on the market. Commercial systems (like Autoform, PAM-Stamp, Stampack, etc.) are, due to their prices, usually beyond financial ability of SME.

Design of the drawing process and tools, i.e. choice of proper values of several design parameters, require efficient optimization strategy. In this process, random character of at least some of the parameters has to be taken into account. In view of this fact, the traditional, deterministic approach to optimization is insufficient and elements of robust design optimization techniques and reliability analysis have to be included in the formulation of the optimization problem. It has to be admitted that, even if some of the mentioned commercial simulation systems offer numerical optimization modules, not all of them reach beyond the deterministic concept of the optimization process.

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

This paper presents basic features of the NUMPRESS system and some examples ofuse. The system has been developed at IPPT PAN as a result of a project financially supported by European Regional Development Fund and is dedicated to small and middle enterprises (SME) dealing with sheet metal forming. The program consists of (i) an analytical finite element method module (ii) an optimization module, (iii) a reliability analysis module, and (iv) a graphical user interface enabling communication between modules. The analytical module consists of two independent programs up to the user’s choice: NUMPRESS-Flow, a faster and less accurate program for implicit quasi-static analysis of rigid-viscoplastic shells (based on the flow approach) and NUMPRESS-Explicit, a program for explicit dynamical analysis of elastic-plastic shells. Both programs are interfaced to a well-known commercial graphical pre-and postprocessor GiD.

sheet metal forming, finite element method, deterministic and robust design optimization, reliability analysis

The objective of the paper is formulation of sensitivity analysis for flow approach simulations of deep drawing problems with respect to arbitrary design parameters. First, finite element formulation of the primary problem is presented. Its important feature is the full algorithmic tangent viscosity matrix which, as it will be shown, is a necessary tool in sensitivity calculations. The algorithmic (consistent) tangent matrix is unfortunately asymmetric, which is addressed in our considerations. The semi-analytical formulation of sensitivity is used, which means that some complex design derivatives in the sensitivity equations are estimated by finite difference method. The finite difference method will be used as a reference method for verification of the sensitivity results.

finite element method, flow approach, sensitivity analysis

finite element method, contact analysis, sheet metal forming

An improved approach to penalty modeling in contact mechanics is proposed. The presented algorithm enables evaluation of the optimum values of the penalty factor for each constrained degree of freedom in the finite element model. The values are chosen so as to ensure desired accuracy in fulfillment of the geometric constraints while keeping the condition number of the modified stiffness matrix at a moderate level. Thus, the main weakness for which the penalty approach is often criticised — excessive worsening of the system conditioning—is fairly limited. Numerical examples confirm advantages of the method.

contact modeling, penalty approach, matrix condition number

In the paper the structural one-dimensional hybrid dynamical model of the entire vibrating rotor-shaft system and the three-dimensional fmite element model of its cracked shaft zone were applied for a fatigue life prediction of the machine faulty segment under coupled bending-torsional-axial vibrations. The steady-state dynamic response amplitudes, obtained by means of the one-dimensional model of the system, have been used for the three-dimensional model as an input data for determination of maximal stresses and stress intensity factors at the crack tip. These quantities together with the Wohler curves enable us an approximate determination of load limits responsible for a probable further crack propagation. By means of the proposed approach one can predict a damage probability of the faulty rotor-shaft system of arbitrary structure operating under various dynamic and quasi-static loads affecting a crack of various sizes and shaft locations. From the investigations performed for various crack axial locations on the shaft with respect to bearing supports of the single- and double-span rotor-shaft systems, it follows that a strength of the cracked zone is much more sensitive to normal stresses due to bending and axial oscillations than to tangential stresses caused by torsional vibrations.

hybrid dynamical mode, vibrating rotor-shaft system, fatigue analysis